Problem: Simplify the following expression: $\dfrac{7q}{4q^4}$ You can assume $q \neq 0$.
Solution: $ \dfrac{7q}{4q^4} = \dfrac{7}{4} \cdot \dfrac{q}{q^4} $ To simplify $\frac{7}{4}$ , find the greatest common factor (GCD) of $7$ and $4$ $7 = 7$ $4 = 2 \cdot 2$ $ \mbox{GCD}(7, 4) = = 1 $ $ \dfrac{7}{4} \cdot \dfrac{q}{q^4} = \dfrac{1 \cdot 7}{1 \cdot 4} \cdot \dfrac{q}{q^4} $ $\phantom{ \dfrac{7}{4} \cdot \dfrac{1}{4}} = \dfrac{7}{4} \cdot \dfrac{q}{q^4} $ $ \dfrac{q}{q^4} = \dfrac{q}{q \cdot q \cdot q \cdot q} = \dfrac{1}{q^3} $ $ \dfrac{7}{4} \cdot \dfrac{1}{q^3} = \dfrac{7}{4q^3} $